Problem: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 8x - 6$ and $ KL = 9x - 15$ Find $JL$.
A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {8x - 6} = {9x - 15}$ Solve for $x$ $ -x = -9$ $ x = 9$ Substitute $9$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 8({9}) - 6$ $ KL = 9({9}) - 15$ $ JK = 72 - 6$ $ KL = 81 - 15$ $ JK = 66$ $ KL = 66$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {66} + {66}$ $ JL = 132$